Are we getting interactions wrong?
The role of link functions
in psychological research

Laura Sità, Margherita Calderan, Tommaso Feraco, Filippo Gambarota, Enrico Toffalini

prima slide

per chi vuole provare a simulare le cose in tempo reale

qr code che manda a questo link https://github.com/sitalaura/link-functions/tree/main/R

oppure scaricare il file a questo percorso sitalaura.github.io/link-functions/R/datasim.R

Example

independent variable: age in years (years)

dependent variable: mistakes in a reading task (errors)

aggiungi screenshot dataset

1 Errors with linear predictor

using the classical linear predictor

fitL = glm(y~age, data=d)

1 Errors with linear predictor SHOW CODE

2 Errors with appropriate model

using the appropriate distribution family=poisson

but, most importantly, the appropriate link link="log"

fitP = glm(y~age, family=poisson(link="log"), data=d)

2 Errors with appropriate model SHOW CODE

3 con effetto interazione

independent variable: age in years (years)

dependent variable: mistakes in a reading task (errors)

adding a new main effect

groups: normal kids (group = 0) vs kids with dyslexia (group = 1)

4 interaction with linear model

an interaction would emerge with a classical linear model (commenta l’output)

fitL_0 = glmmTMB(y ~ age + group + (1|id), data=d)
fitL_1 = glmmTMB(y ~ age * group + (1|id), data=d)
anova(fitL_0, fitL_1)
Data: d
Models:
fitL_0: y ~ age + group + (1 | id), zi=~0, disp=~1
fitL_1: y ~ age * group + (1 | id), zi=~0, disp=~1
       Df    AIC    BIC  logLik deviance Chisq Chi Df Pr(>Chisq)
fitL_0  5                                                       
fitL_1  6 1320.3 1341.5 -654.17   1308.3            1

4 interaction with linear model SHOW CODE

infatti

type I error arriva da 0.05 a 50% sulle interazioni con la link function sbagliata show code (da fare) grafico

Conclusions

conclusioni

Materials & Contact

All materials are available on GitHub at sitalaura/link-functions

Questions and feedbacks laura.sita@studenti.unipd.it

Bibliography

Supplementary materials

wrong family doesnt create issues

if we put the wrong family, but the correct link family=gaussian(link="log") still no interaction (as it should)

fitL_log_0 <- glmmTMB(y ~ age + group + (1|id), family = gaussian(link="log"), data=d, start=list(beta=c(b0, 0, 0)))

fitL_log_1 <- glmmTMB(y ~ age * group + (1|id), family = gaussian(link="log"), data=d, start=list(beta=c(b0, 0, 0, 0)))

anova(fitL_log_0, fitL_log_1)
Data: d
Models:
fitL_log_0: y ~ age + group + (1 | id), zi=~0, disp=~1
fitL_log_1: y ~ age * group + (1 | id), zi=~0, disp=~1
           Df    AIC    BIC  logLik deviance  Chisq Chi Df Pr(>Chisq)
fitL_log_0  5 1228.8 1246.4 -609.41   1218.8                         
fitL_log_1  6 1230.3 1251.5 -609.16   1218.3 0.4946      1     0.4819